A day after a mayoral spokesman said the city was “considering a range of options” when asked about giving taxi medallions to horse-carriage owners, Mayor de Blasio on Thursday denied that the city was weighing such a deal.

But the mayor acknowledged that something “fair” would have to be done to compensate everyone who would lose out under his plan to ban hansom cabs.

New York Mayor Bill de BlasioPhoto: AP

“I’ve said before that we understand in a change like this, we have to be fair to the people who currently have these businesses and do this work,” he said.

“But we also know there are real issues in terms of the values of those current businesses that have to be resolved.”

De Blasio also cited a Wednesday-afternoon incident that left a carriage horse sprawled on a sidewalk near Central Park as a “very simple reason” for why “horses don’t belong on the streets of New York City.”

But a carriage-industry group disputed the mayor’s claim that the horse — a black, 15-year-old gelding named Spartacus — had been “spooked by a bus” at the corner of Central Park West and West 59th Street.

Historic Horse-Drawn Carriages of Central Park said another carriage horse that was “parked” behind Spartacus “unexpectedly pulled out” and accidentally knocked over Spartacus’ carriage, sending him to the ground.

“He did not spook. He did not collapse. Contrary to rumors, he was not startled by a bus,” said Christina Hansen, a driver who helped free Spartacus from his rig.